The OJB's word — "the Dvar HASHEM did mitgashem"
מִתְגַּשֵּׁם
מִתְ־Hitpa'el participle prefix: reflexive, "making oneself"
ג־שׁ־םRoot: body, substance, materiality
־גַּשֵּׁםDoubled middle radical (dagesh in the shin), the intensive stem pattern
Mitgashem: "making himself bodily," "becoming embodied." In the yeshivish idiom of the OJB, "did mitgashem" = הִתְגַּשֵּׁם, he became bodily.
1. The Biblical theology
The Rambam's word for the heresy he condemns is הַגְשָׁמָה (hagshamah), the verbal noun of the hif'il הִגְשִׁים, "to make something bodily." That is the error of men who impose a body on G-d in their idolatrous thinking in wrong-headed corporealism or anthropomorphism and idolatry. But in Daniel, as seen below, worship or service of the Moshiach is not idolatry. (Note carefully: Sanhedrin 98a and also Rashi assert that the Bar Enosh is the Moshiach, see Mikraot Gedolot Daniel 7:13.) But the Word of G-d settles all arguments. In the inerrant Bible the friends of Daniel refuse to PELACH the golden idol but ALL PEOPLES will PELACH the Bar Enosh, who is not an idol (compare Daniel 3:12 and Daniel 7:14). Keil and Delitzsch state that the Aramaic word pelach is used exclusively of service and homage due to G-d in their commentary on Daniel 7:14 (with cross-references to Daniel 3:12–13, 3:17, and Ezra 7:19, 7:24).
The specific location: In the Keil and Delitzsch Commentary on Daniel, under the discussion of Daniel 7:13–14 and Daniel 7:27. The assertion: The authors affirm that pelach (referred to as pelach in Biblical Chaldee / Aramaic) is used IN THE HEBREW BIBLE only for the religious service and reverence rendered to G-d. The way the word is used in the Bible is the inerrant key to its meaning, and we don't go beyond what is written (1 Corinthians 4:6).
The theological application: Keil and Delitzsch apply this to argue that the "one like a son of man" receiving pelach in Daniel 7:14 is granted a universal, everlasting kingdom and divine honor, aligning with the elohut of Moshiach taught elsewhere in the Tanakh (see below). The OJB does not use Rambam's word for the heresy he condemns is הַגְשָׁמָה (hagshamah), the verbal noun of the hif'il הִגְשִׁים, "to make something bodily" but instead answers with the hitpa'el, the reflexive: the Dvar הִתְגַּשֵּׁם — made himself bodily. The same root, two different subjects. In hagshamah, man, in his idolatrous reprobate mind, corporealizes G-d; in mitgashem, the Dvar freely takes on the "ohel" which Kefa refers to as human existence (2Kefa 1:13). Moshiach thereby is tempted in every way as we are, yet without sin (MJ 4:14-16). The Third Ikkar forbids the first: הַגְשָׁמָה (hagshamah), the verbal noun of the hif'il הִגְשִׁים, "to make something bodily."; Yochanan 1:14 proclaims the second: the hitpa'el, the reflexive: the Dvar הִתְגַּשֵּׁם — made himself bodily, took up the ohel of human existence. Similarly, the Kavod took up the Mishkan.
2. In the Tanakh: גְּשֵׁם, "body," in Daniel
The root appears as a noun only in the Aramaic of Daniel, and always means body: the bodies of the three young men that the fire did not touch (3:27, דִּי לָא־שְׁלֵט נוּרָא בְּגֶשְׁמְהוֹן), Nevuchadnetzar's body wet with the dew of heaven (4:30; 5:21), and the body of the fourth beast destroyed (7:11, וְהוּבַד גִּשְׁמַהּ). The decisive verse joins this exhibit's two key words:
וִיהַבוּ גֶשְׁמְהוֹן דִּי לָא־יִפְלְחוּן וְלָא־יִסְגְּדוּן לְכָל־אֱלָהּ לָהֵן לֵאלָהֲהוֹן׃
"They yielded their bodies rather than serve or worship any god except their own G-d" (Daniel 3:28). Chananyah, Mishael, and Azaryah gave their גֶּשֶׁם to the fire to keep their פְּלַח for G-d alone (Room III). Four chapters later, every nation gives that פְּלַח to the Bar Enosh. The One served as G-d in 7:14 is the One who, in Yochanan 1:14, did mitgashem.
3. In the Siddur and the yeshiva: gashmiyus
Medieval Hebrew built on the root: גַּשְׁמִי (material), גַּשְׁמִיּוּת (materiality), הַגְשָׁמָה (corporealization). In Chassidus and in Yiddish, גשמיות (gashmiyes) is the physical world set against רוחניות (ruchniyes), the spiritual. The Chassidic task is to draw ruchniyes down into gashmiyes and make the lower world a דִּירָה בַּתַּחְתּוֹנִים, a dwelling place for Hashem below. The OJB's mitgashem says this happened in person: the Dvar entered gashmiyus and made his dwelling among us.
4. In modern Hebrew: "came true"
Today הִתְגַּשֵּׁם also means "to be realized, to come true," as when a dream or a prophecy materializes. The double sense is exact. When the Dvar did mitgashem, the promise of Shemos 25:8, וְשָׁכַנְתִּי בְּתוֹכָם, came true in the ohel of human existence, as Kefa uses the term in 2Kefa 1:13.
A wordplay to note, not an etymology
Biblical Hebrew גֶּשֶׁם means "rain," and lexicons generally treat it as a separate root from Aramaic "body." Still, the darshan will hear Hoshea 6:3: וְיָבוֹא כַגֶּשֶׁם לָנוּ, "He will come to us like the rain" — Hashem descending from heaven to the earth.